function analysis online practice complete this assessment to review what youve learned. it will not count…

function analysis online practice complete this assessment to review what youve learned. it will not count toward your grade. compare the estimated average rates of change of the functions f(x)=3.5x² and g(x)=3.5ˣ over the interval 1,2.39. (1 point) the average rates of change cannot be compared since f(x) is quadratic and g(x) is exponential. the estimated rate of change of g(x) is greater than the estimated rate of change of f(x) over the interval 1,2.39. the estimated average rates of change of both functions over the interval 1,2.39 are approximately equal. the estimated rate of change of f(x) is greater than the estimated rate of change of g(x) over the interval 1,2.39. check answer remaining attempts : 3

function analysis online practice complete this assessment to review what youve learned. it will not count toward your grade. compare the estimated average rates of change of the functions f(x)=3.5x² and g(x)=3.5ˣ over the interval 1,2.39. (1 point) the average rates of change cannot be compared since f(x) is quadratic and g(x) is exponential. the estimated rate of change of g(x) is greater than the estimated rate of change of f(x) over the interval 1,2.39. the estimated average rates of change of both functions over the interval 1,2.39 are approximately equal. the estimated rate of change of f(x) is greater than the estimated rate of change of g(x) over the interval 1,2.39. check answer remaining attempts : 3

Answer

Explanation:

Step1: Definir la fórmula de tasa de cambio promedio

La tasa de cambio promedio de una función $y = h(x)$ en el intervalo $[a,b]$ es $\frac{h(b)-h(a)}{b - a}$.

Step2: Calcular la tasa de cambio promedio de $f(x)$

Para $f(x)=3.5x^{2}$, $a = 1$, $b = 2.39$. Entonces $f(1)=3.5\times1^{2}=3.5$ y $f(2.39)=3.5\times(2.39)^{2}=3.5\times5.7121 = 19.99235$. La tasa de cambio promedio de $f(x)$ es $\frac{f(2.39)-f(1)}{2.39 - 1}=\frac{19.99235 - 3.5}{1.39}=\frac{16.49235}{1.39}\approx11.865$.

Step3: Calcular la tasa de cambio promedio de $g(x)$

Para $g(x)=3.5^{x}$, $a = 1$, $b = 2.39$. Entonces $g(1)=3.5^{1}=3.5$ y $g(2.39)=3.5^{2.39}$. Usando una calculadora, $3.5^{2.39}\approx30.77$. La tasa de cambio promedio de $g(x)$ es $\frac{g(2.39)-g(1)}{2.39 - 1}=\frac{30.77-3.5}{1.39}=\frac{27.27}{1.39}\approx19.62$.

Step4: Comparar las tasas de cambio

Como $19.62>11.865$, la tasa de cambio promedio estimada de $g(x)$ es mayor que la tasa de cambio promedio estimada de $f(x)$ en el intervalo $[1,2.39]$.

Answer:

The estimated rate of change of $g(x)$ is greater than the estimated rate of change of $f(x)$ over the interval $[1,2.39]$.